Methods and Systems for Fiber Optic Communication

ABSTRACT

The present invention relates in general to communication systems, and more specifically towards methods, systems, and devices that help improve transmission rates and spectral efficiency of intensity modulated (IM) or power modulated channels utilizing multi-level pulse amplitude modulation PAM-M. In an embodiment, the present invention used an iterative algorithm to open the eyes of an eye diagram in a relatively short number of steps. The algorithm, which may not require previous characterization of the channel, utilizes pseudo-random sequences, such as PSBS15 or PRQS10, and adaptive non-linear equalizers to optimize the pre-distortion taps.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/294,965, filed Oct. 17, 2016, which will issue as U.S. patent Ser.No. 10,020,755 on Jul. 10, 2018, the subject matter of which is herebyincorporated by reference in its entirety.

FIELD OF INVENTION

The present invention relates in general to communication systems, andmore specifically towards methods, systems, and devices that helpimprove transmission rates and spectral efficiency of intensitymodulated (IM) or power modulated channels utilizing multi-level pulseamplitude modulation PAM-M.

BACKGROUND

The exponential growth of internet traffic is driving the increase oftransmission data rates in data centers. It is predicted thattransceivers operating at speeds equal or higher than 50 Gbps per lanewill be utilized in high volume by 2020. The predominant optical mediatypes utilized in data centers are multimode and single-mode opticalfibers. The preferred modulation format for transceivers required toachieve data rates higher than 25 Gbps in both fiber types is pulseamplitude modulation (PAM) and in particular PAM-4. For directlymodulated vertical-cavity surface-emitting laser (VCSEL) basedtransceivers, the implementation of PAM-4 at data rates over 50 Gbps ischallenging due to the slow and non-linear response of the laser. Thisslow and non-linear response results in signal degradation exhibitableby uneven and/or skewed eyes in an eye diagram.

Thus, there exists a need for further development of methods, systems,and devices which optimize optical signal transmission at high datarates (e.g., at or over 50 Gbps) reducing optical penalties caused bychannel impairments such as laser jitter, laser eye tilt, opticaldispersion, and distortion among others.

As such, there is a need for further development of devices, systems,and methods which attempt to reduce optical penalties caused by channelimpairments such as laser jitter, laser eye tilt, optical dispersion,and distortion among others.

SUMMARY

Accordingly, disclosed herein are embodiments of devices, systems, andmethods which attempt to reduce optical penalties caused by channelimpairments such as laser jitter, laser eye tilt, optical dispersion,and distortion among others.

In an embodiment, the present invention provides a method and apparatusfor optimizing/tuning data transmission over optical channels where onlythe power or intensity of the signals can be modulated.

In another embodiment, the present invention is an iterative method ofoptimizing the pre-distortion and correction for eye diagram skew.

In yet another embodiment, the present invention is directed towardsusing an iterative algorithm to open the eyes of an eye diagram in arelatively short number of steps. The algorithm, which may not requireprevious characterization of the channel, utilizes pseudo-randomsequences, such as PSBS15 or PRQS10, and adaptive non-linear equalizersto optimize the pre-distortion taps.

In still yet another embodiment, the present invention is an opticalcommunication system for transmitting a communication signal. Theoptical communication system comprises a first transceiver; a secondtransceiver; an optical medium for transmitting the communication signalbetween the first transceiver and the second transceiver; apre-distortion circuit for conditioning the communication signal priorto a transmission of the communication signal by the first transceiver,the pre-distortion circuit providing linear correction of thecommunication signal; a post-equalization circuit for conditioning thecommunication signal after a receipt of the communication signal by thesecond transceiver, the post-equalization circuit providing linearcorrection of the communication signal, at least one of thepre-distortion circuit and the post-equalization circuit furtherproviding non-linear correction of the communication signal; and afeedback circuit providing at least some information from thepost-equalization circuit to the pre-distortion circuit.

In still yet another embodiment, the present invention is a method oftuning a fiber optic communication system. The method includes the stepsof:

(a) generating a source signal X;

(b) pre-distorting the source signal X by applying at least onepre-distortion equalizer to the source signal X to generate apre-distorted signal X_(P) ^(i);

(c) transmitting the pre-distorted signal X_(P) ^(i) over an opticalchannel to generate a transmitted signal Y^(i);

(d) post-equalizing the transmitted signal Y^(i) by applying at leastone post-equalization equalizer to the transmitted signal Y^(i) togenerate a post-equalized signal Z^(i);

(e) evaluating the post-equalized signal Z^(i) to determine aperformance of the fiber optic communication system; and

(f) when the performance of the fiber optic communication system failsto meet a predefined threshold, updating the at least one pre-distortionequalizer and repeating steps (b)-(f), wherein i represents an indextracking each cycle of performing the steps (b)-(f).

In still yet another embodiment, the present invention is an opticaltransceiver configured to at least one of transmit and receive acommunication signal. The optical transceiver comprises: apre-distortion circuit for conditioning the communication signal priorto a transmission of the communication signal by the opticaltransceiver, the pre-distortion circuit providing linear correction ofthe communication signal; a post-equalization circuit for conditioningthe communication signal after a receipt of the communication signal bythe optical transceiver, the post-equalization circuit providing linearcorrection of the communication signal, at least one of thepre-distortion circuit and the post-equalization circuit furtherproviding non-linear correction of the communication signal; and afeedback circuit for providing at least some information from thepost-equalization circuit to a secondary pre-distortion circuit of asecondary optical transceiver.

In still yet another embodiment, the present invention is an opticalcommunication system which comprises:

(a) means for generating a source signal X;

(b) means for pre-distorting said source signal X by applying at leastone pre-distortion equalizer to said source signal X to generate apre-distorted signal X_(P) ^(i);

(c) means for transmitting said pre-distorted signal X_(P) ^(i), over anoptical channel to generate a transmitted signal Y^(i);

(d) means for post-equalizing said transmitted signal Y^(i) by applyingat least one post-equalization equalizer to said transmitted signalY^(i) to generate a post-equalized signal Z^(i);

(e) means for evaluating said post-equalized signal Z^(i) to determine aperformance of said fiber optic communication system; and

(f) means for updating said at least one pre-distortion equalizer andreinvoking means (b)-(f) when said performance of said fiber opticcommunication system fails to meet a predefined threshold,

wherein i represents an index tracking each cycle of invoking means(b)-(f).

In still yet another embodiment, the present invention is a transceiverapparatus that includes: at least one processor capable of computing andapplying linear and non-linear pre-distortion and post-equalization,circuits to perform ADC and DAC functionalities, clock recovery, laserdriver, analog filters and amplifier, transmitter and receiver opticalsubassembly including laser and photodetectors with bandwidths equal orhigher than 16 GHz. In a variation of this embodiment, the processorassigned to code and decode transmitter and receiver signals cansynchronize, mathematically transform, and compare transmitted andreceived signals in order to update equalizer tap coefficients. In yetanother variation, the processor is connected to an internal temperaturesensor and has means to estimate the bias current or voltage applied tothe laser. In still another variation, the processor(s) can connect toan external controller that regulate operational conditions such astemperature, in order to estimate the optimum equalization schemes for agiven range of temperatures. In still yet another variation, theprocessor(s) can store information regarding optimum linear andnon-linear equalization configuration for a given set of operationalconditions (e.g., temperature or bias current). In still yet anothervariation, the processor(s) are able to retrieve stored informationregarding optimum linear and non-linear equalization configuration for agiven set of operational conditions, and modify equalization schemesgradually while minimizing BER. In still yet another variation, theprocessor at the transmitter uses sin c, raised cosine, Gaussian, or erfpulses with amplitude levels that do not map with the original PAMsignal levels, producing a distorted signal with a closed eye diagrambefore the laser or before the post-equalization performed at thereceiver. In still yet another variation, the processor at thetransmitter uses polynomial functions, where the argument of thosefunctions is the level of the original signal, in order to vary thetiming of sin c, raised cosine, Gaussian, or erf pulses producing a datadependent jitter that compensate for the jitter produced by the timevariant response of the laser. In still yet another variation, theprocessor at the transmitter uses signal dependent equalizer, where thetaps depend on original signal levels in order to pre-distort the signalbefore is sent to the laser. In still yet another variation, theprocessor at the receiver uses a signal dependent equalizer, where thetaps depend on signal recovered after ADC, in order to post-distort thesignal before decoding.

Advantageous embodiments of the invention are based upon the inventors'recognition that current methods to characterize the laser response,i.e. S-parameters, are inaccurate when correcting the channel due to thenon-linear time variant response of the laser. The inventors disclose aniterative approach to open the eye of an eye diagram and/or tominimize/reduce transmission bit error ratio (BER) using a combinationof linear and non-linear equalization.

These and other features, aspects, and advantages of the presentinvention will become better understood with reference to the followingdrawings, description, and any claims that may follow.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a block diagram of transmission channel, according toan embodiment of the present invention.

FIG. 2A illustrates an exemplary eye diagram which exhibits skew/tilt.

FIG. 2B illustrates an exemplary eye diagram which has been correctedfor skew/tilt.

FIG. 3 illustrates a flow diagram of a method of optimizing an opticaltransmission system, according to an embodiment of the presentinvention.

FIGS. 4A and 4B illustrate exemplary eye diagrams used in thecalculation of a non-linear equalizer, according to an embodiment of thepresent invention.

FIG. 4C illustrates the profiles of the eyes shown in FIGS. 4A and 4B.

FIG. 5A illustrates exemplary plots representing the shape of signalpulses shown in FIG. 4C.

FIGS. 5B-5D illustrate exemplary procedures to obtain the eye diagramskew/tilt correction.

FIG. 6 illustrates a flow diagram of a method of optimizing an opticaltransmission system, according to an embodiment of the presentinvention.

FIG. 7 illustrates an exemplary implementation of system tuning, inaccordance with an embodiment of the present invention, for a VCSELoperating at 56 Gb/s with high bias voltage.

FIG. 8 illustrates an exemplary implementation of system tuning, inaccordance with an embodiment of the present invention, for a VCSELoperating at 56 Gb/s with low bias voltage.

FIG. 9 illustrates an exemplary implementation of system tuning, inaccordance with an embodiment of the present invention, for a VCSELoperating at 64 Gb/s with high bias voltage.

FIG. 10 illustrates an exemplary implementation of system tuning, inaccordance with an embodiment of the present invention, for a VCSELoperating at 70 Gb/s with high bias voltage.

DETAILED DESCRIPTION

The following description is provided with reference to a VCSEL as anoptical source and PAM-4 as the modulation format. However, it should beapparent that these references are exemplary, and the inventionsdescribed herein may be applicable to other modulation formats and maybe used with other (laser and non-laser) optical sources.

Referring now to FIG. 1, said figure illustrates a block diagram of theprimary components of a fiber transmission channel in accordance with anembodiment of the present invention. At input 100 data is transmitted ina binary or multilevel electrical signal format to the processor 102.The processor 102 uses the input sequence bits to form the required PAMsignal. For example, if the input is a binary signal and the requiredtransmission signaling format is PAM-4, the processor will assign twobits for each PAM-4 level. Processor 102 can use Gray coding to reduceerrors in the detection of the signal and can oversample the signalusing interpolation to estimate the signal values at times that areproportional to fraction of the symbol duration. The symbol duration (7)is estimated from the Baud rate using:

T=Baud_Rate⁻¹  (1)

Processor 102 further pre-distorts the signal to accommodate for thelaser's linear and nonlinear impairments. The computation of parametersutilized for the pre-distortion is explained further in thespecification.

The signal generated by the processor 102 is fed into a digital toanalog converter (DAC) 104 circuit to convert the digital bits to ananalog signal. Next, the analog signal is transmitted to a laser driver,amplifier, and filters 106 used to clean the analog electrical signal.Thereafter, a VCSEL 108 is used to convert the analog electrical signalto an optical signal which is coupled to a multimode optical fiber (MMF)110 using a lens or diffractive optics device. During propagationthrough the fiber, the optical signal is effected by modal and chromaticdispersion as well as attenuation. Upon arrival at the opposite end ofthe fiber, the optical signal is detected by a photo-detector 112 whichconverts the optical signal to an electrical signal which is thenamplified by way of a trans-impedance amplifier. Next, an analog frontend 114 consisting of a continuous time linear equalizer (CTLE) and gaincontrol amplifiers are used to correct and amplify the electrical signalto a required voltage to reduce or minimize quantization noise. Lastly,an analog digital converter (ADC) 116 converts the analog electricalsignal to a digital electrical signal and processor 118 uses the digitalsignal to recover the original input information 100.

The corrective methods, described herein, used to improve the quality ofsignal transmission may be performed using processor 102 (located in thetransmitter), processor 118 (located in the receiver), and/or by usingan external processor dedicated to optimizing the pre-distortion of thelaser or post-equalizing the received signal. It's worth noting that inpractice, many of today's optical communication devices include bothtransmitter and receiver packaged together in a single device(transceiver). As such, processors 102 and 118 are likely to be locatedin the same transceiver and will likely correspond to the same circuit.Thus, the separation between processors 102 and 118 is providedprimarily to emphasize the different functions perform during theoptimization of the equalizer or during the operation of thetransceiver.

To obtain preferred results, the corrective technique described hereincorrect for at least one of linear and non-linear impairments. For thelinear components, one may use the minimum mean square equalizer withsymbol spaced or fractional spaced taps. The equalization is typicallyapplied at the receiver or transmitter to correct for inter-symbolinterference (ISI). However, due to the non-linear and time variantresponse of multimode lasers, this linear approach is not efficient.This deficiency can be dealt with by distributing the linearequalization load among the transmitter and receiver. Such distributionis achieved by gradually varying the coefficients of the linearequalizer according to the signal eye diagram or BER estimated at thereceiver. At each step, the linear equalizer is updated according to aset of rules and equations described herein. The linear equalizerimplemented here, using the disclosed method, may produce a significantimprovement in the signal eye diagram and BER. However, linearequalization alone has limitations for correcting other impairmentscaused by the non-linear response of the VCSEL, such as uneven signallevel separation or eye diagram tilt.

An example of eye diagram tilt is shown in FIG. 2A which illustrates aneye diagram obtained at the receiver without any skew compensation. Asevident from this illustration, top middle, and bottom eyes 201, 203,205, respectively, exhibit a skew (shift relative to a vertical axis)relative to one another. To help correct such impairment, a non-linearequalizer is added as part of the corrective approach. It is computedusing pre-determined functions that alter the shape of the pulse anddistort the temporal sampling, producing the aligned eye diagram shownin FIG. 2B where top, middle, and bottom eyes 207, 209, 211 aresubstantially aligned.

FIG. 3 illustrates a flowchart representative of an algorithm whichembodies the method of signal correction (also referred to as“training”) in accordance with embodiments of the present invention.Each cycle or iteration of the algorithm is tracked by an indexrepresented by the variable i.

Embodiment 1

In step 301, a non-distorted multi-level signal X that is based on apseudo-random sequence is generated. Next, in step 303 a pre-distortedsignal, X_(P) ^(i), is computed using:

X _(P) ^(i) =c _(L) ^(i) ⊗X⊗c _(NL) ^(i)(X)  (2)

where c_(L) ^(i), c_(NL) ^(i) are vectors that represent the linear andnon-linear equalizers, respectively, and the second convolution correctsfor the non-linearities produced by the laser, such as uneven signallevel separation or eye diagram skew. At the beginning of theoptimization process (i.e., i=0) the central taps of the linear andnon-linear equalizers are set to one, and all other taps are set tozero.

Once the pre-distorted signal is generated in step 305, this signalX_(P) ^(i) is sent through the channel. In an embodiment, a channel caninclude all the components that are between the processors 102 and 118(see FIG. 1). For example, this channel includes the DAC 104, laserdriver 106, VCSEL 108, fiber 110, photo detector 112, analog front end114, and ADC 116. The digitized signal arriving at processor 118 islabeled Y^(i). During training, both X and Y^(i) are known at thereceiver.

After traversing the channel, the signal is evaluated and in step 307linear equalizer taps are computed. In an embodiment, minimum meansquare error (MMSE) is used to compute linear equalizer taps by:

b _(L) ^(i)=(R _(xx) ⁻¹ +H ^(h) R _(nn) ⁻¹ H)⁻¹ H ^(h) R _(nn) ⁻¹  (3)

where, R_(xx)=E{XX^(h)}, E{ } represent the ensemble mean valueoperator, R_(nn) is the correlation matrix of the noise, and H is amatrix that represent the channel response. The computed taps are thenused for the correction of the linear response which is given by:

Z ^(i) =b _(L) ^(i) ⊗Y ^(i)  (4)

Also, in step 307, the non-linear equalizer is computed. In anembodiment, the computation of the non-linear equalizer is performedonly once at the beginning of the cycle, when i=0. In anotherembodiment, the non-linear equalizer is computed upon every iteration ofthe algorithm. In yet another embodiment, the non-linear equalizer iscomputed more than once, but not necessarily during every cycle of thealgorithm (e.g., every other cycle, every third cycle, every fourthcycle, or in any desired sequence).

An example of the non-linear equalizer computation is provided withreference to a PAM-4 signal transmitted at a rate of 56 Gbps andrepresented in FIGS. 4A-4C. FIG. 4A illustrates an initial eye diagramobtained from the PAM-4 signal Y^(i) transmitted over a channel. In thisfigure, the top, middle, and bottom eyes are indicated by referencenumerals 501, 503, and 505, respectively. The eye diagram is stored in amatrix and normalized to the peak value. Next, it is inverted bysubtracting 1 from all its elements. The inverted matrix, along with theinverted top, middle, and bottom eyes which are referenced as 507, 509,and 511, respectively, is shown in FIG. 4B. Using the inverted matrix,the amplitude profiles of these inverted eyes are computed. The profilesfor the top, middle, and bottom eyes are represented by the 513, 515,and 517 traces in FIG. 4C. Once the profiles are available, the width ofeach profile is computed using:

$\begin{matrix}{{Width}_{j} = {\sqrt{\frac{\sum\limits_{v_{y}}{{{profile}_{j}\left( v_{y} \right)}v_{y}^{2}}}{\sum\limits_{v_{y}}{{profile}_{j}\left( v_{y} \right)}}}.}} & (5)\end{matrix}$

where j is an index variable for the top, middle, or bottom eye. Thelevels of the PAM-M signal are corrected using functions that depend onthe width variations. For example, using PAM-4, one can use:

Levels=[0,0.333,0.666,1]−Δ([0,Width₁,Width₂,Width₃]−min(Width₁,Width₂,Width₃))  (6)

Additionally, in step 307, the parameters to correct for the eye diagramskew are also computed using:

b _(NL) ^(i)(Y ^(i))=ƒ(g(Y ^(i)))  (6)

where ƒ(.) is a function array that estimates the signal pulse shape andg(.) represents a function array that estimates the eye diagram skew.Typical functions for ƒ(.) contemplated in this disclosure are the sincfunction, raised cosine function, and Gaussian pulse shape and errorfunction (erf) pulse. For example, when using the raised cosinefunction, ƒ(.) is given by:

$\begin{matrix}{{f(a)} = \left\{ \begin{matrix}{\frac{\pi}{4}\sin \; {c\left( \frac{1}{2\beta} \right)}} & {a = {\pm \frac{1}{2\beta}}} \\{\sin \; {c(a)}\frac{\cos \left( {{\pi\beta}\; a} \right)}{1 - \left( {2\beta \; a} \right)^{2}}} & {otherwise}\end{matrix} \right.} & (7)\end{matrix}$

where a is the function argument and β is the roll-off factor thatrepresents the excess bandwidth of the filter from 0 to 1. Exemplaryresults of using three typical ƒ(a) functions to estimate a signal pulseshape are shown in the plots of FIG. 5A.

As for functions g(.), these functions can be obtained from the invertedeyes 507, 509, and 511, shown in FIG. 4B. FIGS. 5B-5D show theapplication of different functions to the eye diagram of FIG. 4B toestimate the eye tilt/skew. For example, in FIG. 5B, the centroids ofthe top, middle, and bottom inverted eyes are computed and a linearpolynomial fitting function is obtained. Therefore, g(.) can be definedby:

$\begin{matrix}{{g(a)} = {\sum\limits_{k = 0}{h_{k}a^{k}}}} & (8)\end{matrix}$

Continuing with the example of FIG. 5B, which shows a linear estimatorfor the eye diagram skew as

g(a)=h ₁ a+h ₀  (9)

using h₀=0 to avoid corrections in the middle eye and assuming anon-linear equalizer with 2 taps, the equalization coefficients aregiven by:

b _(NL) ^(i)(Y ^(i))=[ƒ(1−h ₁ Y ^(i) /T),ƒ(Y ^(i) /T)]  (10)

FIGS. 5C and 5D apply a similar approach but instead of obtaining alinear polynomial fitting function, the function of FIG. 5C is aquadratic polynomial fitting function and the function of FIG. 5D is atruncated cubic polynomial fitting function.

Referring back to FIG. 3, upon completion of post-equalization, in step308 the performance of the system is estimated. In an embodiment, thisis done by computing the BER which can be based on the eye diagram or bybit-to-bit comparison of signals X and Z^(i). If the computed BER iswithin a preset threshold or if the computed BER is worse than the BERof a previous iteration (considered for second or higher cycles of thealgorithm), the algorithm cycle is terminated and the system is thenconsidered ready for communication. If, on the other hand, the computedBER is lower than the BER obtained in previous iterations, the filtertaps are updated in step 310. For the linear component, the vectorsupdate can be obtained using:

c _(L) ^(i) =A(c _(L) ^(i-1) ⊗b _(L) ^(i-1))+(1−A)(c _(L) ^(i-1))  (11)

where A is a weight factor which takes on values between 0 and 1, andregulates the update speed of the equalizer, and b_(L) ^(i) is a vectorthat represent the linear equalizer computed earlier. Likewise, for thenon-linear component, the vectors update can be obtained by:

c _(NL) ^(i)(X)=ƒ(g(X))  (12)

Once the equalizer taps and functions are updated, a new pre-distortedsignal is generated in step 303 and the cycle continues until the BERfloors are reached or until a target BER is achieved. In someembodiments, the optimization requires less than 10 iterations.

Embodiment 2

In an alternate embodiment of the present invention, the disclosedmethod is modified as follows. For the sake of convenience, reference isagain made to the steps of FIG. 3. However, the content of those stepshas been modified at least partially relative to the previouslydiscussed embodiment.

In step 301, a non-distorted multi-level signal X that is based on apseudo-random sequence is generated. Next, in step 303 a pre-distortedsignal, X_(P) ^(i), is computed using:

X _(P) ^(i) =c _(L) ^(i) ⊗X  (13)

where c_(L) ^(i) is a vector that represents the linear equalizer. Atthe beginning of the optimization process (i.e., i=0) the central tap ofthe linear equalizer is set to one, and all other taps are set to zero.Once the pre-distorted signal is generated in step 305, this signalX_(P) ^(i) is sent through the channel, arriving at processor 118 assignal Y^(i). During training, both X and Y^(i) are known at thereceiver.

After traversing the channel, the signal is evaluated and in step 307the linear and non-linear equalizers are computed resulting in b_(L)^(i) and b_(NL) ^(i) (Y^(i)) vectors. In an embodiment, the linear andnon-linear equalizers are computed pursuant to the same calculations asdetailed in Embodiment 1. Likewise, as in Embodiment 1, the computationof the non-linear equalizer may be performed only once at the beginningof the cycle (i.e., when i=0), upon every iteration of the algorithm, ormore than once, but not necessarily during every cycle of the algorithm(e.g., every other cycle, every third cycle, every fourth cycle, or inany desired sequence).

The computed taps are then used for the correction of the linearresponse which is given by:

Z ^(i) =b _(L) ^(i) ⊗Y ^(i) ⊗b _(NL) ^(i)(Y ^(i))  (14)

Referring back to FIG. 3, upon completion of post-equalization, in step308 the performance of the system is estimated. In an embodiment, thisis done by computing the BER which can be based on the eye diagram or bybit-to-bit comparison of signals X and Z^(i). If the computed BER iswithin a preset threshold or if the computed BER is worse than the BERof a previous iteration (considered for second or higher cycles of thealgorithm), the algorithm cycle is terminated and the system is thenconsidered ready for communication. If, on the other hand, the computedBER is lower than the BER obtained in previous iterations, the linearfilter taps are updated in step 310 using equation (11). Once theequalizer taps are updated, a new pre-distorted signal is generated instep 303 and the cycle continues until the BER floors are reached oruntil a target BER is achieved. In some embodiments, the optimizationrequires less than 10 iterations.

Embodiment 3

In yet another embodiment of the present invention, the disclosed methodis modified as follows. As previously, for the sake of convenience,reference is again made to the steps of FIG. 3. However, the content ofthose steps has been modified at least partially relative to thepreviously discussed embodiments.

In step 301, a non-distorted multi-level signal X that is based on apseudo-random sequence is generated. Next, in step 303 a pre-distortedsignal, X_(P) ^(i), is computed using equation (2). At the beginning ofthe optimization process (i.e., i=0) the central taps of the linear andnon-linear equalizers are set to one, and all other taps are set tozero. Once the pre-distorted signal is generated in step 305, thissignal X_(P) ^(i) is sent through the channel, arriving at processor 118as signal Y^(i). During training, both X and Y^(i) are known at thereceiver.

After traversing the channel, the signal is evaluated and in step 307the linear and non-linear equalizers are computed resulting in b_(L)^(i) and b_(NL) ^(i) (Y^(i)) vectors. In an embodiment, the linear andnon-linear equalizers are computed pursuant to the same calculations asdetailed in Embodiment 1. Likewise, as in Embodiment 1, the computationof the non-linear equalizer may be performed only once at the beginningof the cycle (i.e., when i=0), upon every iteration of the algorithm, ormore than once, but not necessarily during every cycle of the algorithm(e.g., every other cycle, every third cycle, every fourth cycle, or inany desired sequence). The computed taps are then used for thecorrection of the linear response pursuant to equation (14) resulting insignal Z^(i).

Referring back to FIG. 3, upon completion of post-equalization, in step308 the performance of the system is estimated. In an embodiment, thisis done by computing the BER which can be based on the eye diagram or bybit-to-bit comparison of signals X and Z^(i). If the computed BER iswithin a preset threshold or if the computed BER is worse than the BERof a previous iteration (considered for second or higher cycles of thealgorithm), the algorithm cycle is terminated and the system is thenconsidered ready for communication. If, on the other hand, the computedBER is lower than the BER obtained in previous iterations, the linearfilter taps are updated in step 310 using equations (11) and (12). Oncethe equalizer taps and functions are updated, a new pre-distorted signalis generated in step 303 and the cycle continues until the BER floorsare reached or until a target BER is achieved. In some embodiments, theoptimization requires less than 10 iterations.

Since the operation of a laser optical source may be affected, to somedegree, by temperature or bias current variations, it may beadvantageous to estimate and store the optimum equalizer parameters fora range of operational conditions (e.g. range of temperatures in datacenters). FIG. 6 shows flowchart representative of a method based on theequalizer optimization algorithm disclosed earlier to evaluate and storethe preferred or optimum equalization parameters for a required range ofoperational conditions.

In this method, the optimum equalization parameters for severalenvironmental conditions (e.g., temperature and or bias current) aremeasured for a set of lasers representative of a fabricated batch. Ashort link of multimode fiber (e.g. 1 m) can be used in order to isolatethe pre-distortion equalizer optimization to the channel response due tothe fiber and receiver. The advantage of using a short fiber link isthat the pre-distortion can primarily be dedicated to correcting thelaser response of the representative laser while neglecting themodal-chromatic dispersion of the fiber and other laser impairments dueto the normal laser fabrication process which can be corrected by thepost-equalizer at the receiver. Using this method, the laser correction,especially the non-linear correction component, can be performed duringoperation and changed rapidly according to environmental conditions,while the post-equalizer can adapt to different length of fibers orbatch variations.

Referring to FIG. 6, the procedure begins in step 701 where the laser ortransceiver is turned on with a specified bias voltage in a temperaturecontrolled environment. In step 703 the algorithm represented in FIG. 3is performed in order to find the optimum linear and non-linearequalizer. Next, in step 705 the optimum equalization parameters arestored. Thereafter, the operational conditions, (e.g., temperatureand/or bias current) are changed within a pre-determined range and thecycle is repeated until all desired operational conditions in thespecified range are tested. Once the test finalizes, the stored optimumequalization parameters are transferred to memory in the transceiverprocessor (102 and 108) for use during operation.

Implementation of the method described herein has been achieved using anarbitrary waveform generator (AWG) and real time scope (RTS) capable of100 GSa/s. A program running on an external computer controlled the AWGand RTS as well as the voltage sources, laser, and photodetector.Several VCSELs with operating wavelengths of 850 nm and 980 nm and PAM-4modulation format were used to transmit at data rates over 50 Gbps andBER<1e-4, which are low enough to produce a post forward errorcorrection (FEC) BER<1e-15 when RS(544,514) or better FEC is utilized.FIGS. 7-10 serve to illustrate several stages of the algorithmimplementation. FIGS. 7 and 8 show PAM-4 transmission eyes for 56 Gb/susing two bias voltages, 2.5 V and 2.3 V. FIGS. 9 and 10 show PAM-4transmission using a 2.5 V bias voltage at two data rates: 64 Gbps and70 Gbps.

For exemplary purposes the number of taps on the experiments was fixedto 13 and fractional spaced sampling was used. In addition, all examplesuse the same physical optical link which included 100 m of highbandwidth modal-chromatic dispersion compensating OM4 fiber.

FIGS. 7-10 each show 4 vertical columns, where the eye diagrams ofsignals {X, X_(P) ^(i), Y^(i), Z^(i)} are compared. The signaltransmitted without pre-distortion, X, is shown in the first column, thesignal transmitted with pre-distortion, X_(P) ^(i), is shown in thesecond column, the received signal without post-equalization, Y^(i), isthe third column, and the post-equalized signal, Z^(i) is the fourthcolumn. The rows represent the resultant eye diagrams according to theprocessing process represented in FIG. 3 at several stages. The firstrow, i=0, shows the eye diagrams during the first iteration. The secondrow is the last iteration when the non-linear component of the equalizeris turned off. The third row shows the eye diagrams for the finaliteration when the non-linear correction is implemented.

The improvements at each stage due only to linear post equalization,pre-distortion, or both can be observed in each figure. For example,image (805) in FIG. 7 shows the eye diagram without pre-distortion andwithout post-equalization for 56 Gbps using a 2.5 bias voltage. The BERfor this eye diagram is greater than 2e-2. Image (807) shows the eyediagram when only linear post-equalization is applied. This imageindicates that the eye diagram can be improved producing a BER of≈4.5e-5. Image (815) shows the final iteration of the proposed algorithmwhen the eye skew correction is turned off. In that case, since theequalization is shared by the transmitter and receiver the BER reducesto ≈2.1e-5. Image (823) shows the final results when the eye diagramskew correction as disclosed in the present invention is turned on. Inthis case the BER reduces to ≈7.8e-6.

FIG. 8 uses the same laser operating with a lower bias voltage (2.3V),which effectively reduces the bandwidth and increases the eye diagramtilt. Image (905), shows the eye diagram without pre-distortion andwithout post-equalization for 56 Gb/s, which produces a BER of ≈7.9e-2.Image (907) shows the eye diagram when only linear post-equalization isapplied, which produces a BER of ∓3.2e-3. Image (915) shows the finaliteration of the proposed algorithm when the eye skew correction isturned off. In that case, since the equalization is shared by thetransmitter and receiver, the BER reduces to ≈4.1e-4. Image (923) showsthe final results when the eye diagram skew correction disclosed in thepresent invention, is turned on. In this case the BER reduces to≈8.6e-5.

Image (1005) in FIG. 9, shows the eye diagram without pre-distortion andwithout post-equalization for 64 Gbps using 2.5 bias voltage. This eyediagram produces BER of ≈3e-2. Image (1007) shows the eye diagram whenonly linear post-equalization is applied, which produces a BER of≈4.5e-4. Image (1015) shows the final iteration of the proposedalgorithm when the eye skew correction is turned off, which produces aBER of ≈3.5e-5. Image (1023) shows the results when the eye diagram skewcorrection disclosed in the present invention is turned on, whichproduces a BER reduces to ≈1.3e-5.

Lastly, image (1105) in FIG. 10 shows the eye diagram withoutpre-distortion and without post-equalization for 70 Gbps using 2.5 biasvoltage. This eye diagram produces a BER of ≈1e-3. Image (1107) showsthe eye diagram when only linear post-equalization is applied, whichreduces the BER to ≈9e-4. Image (1115) shows the final iteration of theproposed algorithm when the eye skew correction is turned off producinga BER of ≈6.6e-5. By turning on the eye diagram skew correction the BERreduces to ≈3.2e-5.

Note that while this invention has been described in terms of severalembodiments, these embodiments are non-limiting (regardless of whetherthey have been labeled as exemplary or not), and there are alterations,permutations, and equivalents, which fall within the scope of thisinvention. Additionally, the described embodiments should not beinterpreted as mutually exclusive, and should instead be understood aspotentially combinable if such combinations are permissive. It shouldalso be noted that there are many alternative ways of implementing themethods and apparatuses of the present invention. It is thereforeintended that claims that may follow be interpreted as including allsuch alterations, permutations, and equivalents as fall within the truespirit and scope of the present invention.

We claim:
 1. An optical communication system for transmitting acommunication signal, said optical communication system comprising: afirst transceiver; a second transceiver; an optical medium fortransmitting said communication signal between said first transceiverand said second transceiver; a pre-distortion circuit for conditioningsaid communication signal prior to a transmission of said communicationsignal by said first transceiver, said pre-distortion circuit providinglinear correction of said communication signal; a post-equalizationcircuit for conditioning said communication signal after a receipt ofsaid communication signal by said second transceiver, saidpost-equalization circuit providing linear correction of saidcommunication signal, at least one of said pre-distortion circuit andsaid post-equalization circuit further providing non-linear correctionof said communication signal; and a feedback circuit providing at leastsome information from said post-equalization circuit to saidpre-distortion circuit.
 2. The optical communication system of claim 1,further comprising a performance estimation circuit, said performanceestimation circuit evaluating said communication signal after it hasbeen conditioned by said post-equalization circuit.
 3. The opticalcommunication system of claim 2, wherein said performance estimationcircuit calculates a bit error rate (BER) of said communication signalafter it has been conditioned by said post-equalization circuit.
 4. Theoptical communication system of claim 1, wherein said pre-distortioncircuit conditions said communication signal by convolving saidcommunication signal with a linear equalizer vector.
 5. The opticalcommunication system of claim 4, wherein said pre-distortion circuitfurther conditions said communication signal by convolving saidcommunication signal with a non-linear equalizer.
 6. The opticalcommunication system of claim 1, wherein said post-equalization circuitconditions said communication signal by convolving said communicationsignal with a linear equalizer vector.
 7. The optical communicationsystem of claim 6, wherein said post-equalization circuit furtherconditions said communication signal by convolving said communicationsignal with a non-linear equalizer.
 8. The optical communication systemof claim 1, wherein said linear correction provided by saidpre-distortion circuit depends at least partially on said at least someinformation provided by said feedback circuit.
 9. The opticalcommunication system of claim 1, wherein said system is configured tooperate using pulse amplitude modulation (PAM).
 10. The opticalcommunication system of claim 9, wherein said PAM is PAM-4.